They didn't prove anything except that by increasing the complexity of 'Life', they can force some kind of complex behaviour that would have been impossible for the simpler version we're all more familiar with. They changed the rules from 'alive or dead' tiles to '00 01 10 or 11' tiles. There are two different rhomboids in the Penrose tile universe they're playing in, so it seems to make sense that you will find some sufficiently complex means of navigating it if you observe two bits at once.

I think it should have been couched differently: Penrose universe NOT non-repeating, given a sufficiently complex, self-changing pattern to look for.

Gliders are commonplace on repeating grids. According to TFA (and this makes sense), it was thought that they could not be made on non-repeating grids. After all, which direction should it follow? How to make sure it can even exist in the place it will move to?

However, I feel that by allowing more types of tiles, it should be clear that it was possible. For example, with four types of cells, you could have "front of glider" (becomes "back of glider")"back of glider" (becomes "not glider") "side of glider" to keep the rest in check (keeps status unless in contact with "back of glider", when it becomes "not glider") "not glider" (becomes "side of glider" if in contact with one "side of glider" and one "front of glider", becomes "front of glider" if in contact with two "side of glider" and no "back of glider")